Barcelona is superb, with an excellent, modern (and fully-integrated) public transport system. Most of the main tourist areas are very flat, so there would be no problems with getting around.
The city is a paradise for shopaholics and lovers of fine foods, with plenty of cultural and historic attractions as well. You certainly wouldn't be stuck for something to do!
While your mother might hate beach holidays, she might still enjoy the excellent paella served at one of Barcelona's many beach-side bars and restaurants.
There are loads of cheap flights to Barcelona. Many people choose to fly to Gerona or Reus (with Ryanair) and then take the direct bus into the city from there but, with your mother's limited mobility, it would probably make more sense to fly directly to Barcelona (El Prat) Airport with BA (from Heathrow or London City), Jet2 (from Glasgow, Leeds/Bradford or Manchester), Monarch (from Gatwick, Manchester or Birmingham), Ryanair (from Edinburgh, Prestwick, Liverpool, Stansted or East Midlands) or easyJet (from Belfast, Bristol, Liverpool, Gatwick, Luton, Southend, Stansted or Newcastle).
El Prat Airport has very easy access to the city centre by both rail and bus:
http://www.aena-aerop...Public-transport.html
but, given the proximity of the airport to the city centre, a taxi probably wouldn't cost much anyway.
Start your accommodation search here:
http://www.tripadviso...Catalonia-Hotels.html
Find out what the city has to offer here:
http://www.barcelonaturisme.com/English/
Chris